Spatial harmonic traveling wave tube



Jan. 14, 1958 v s. D. ROBERTSON SPATIAL HARMONIC TRAVELING WAVE TUBEFiled Dec. 30, 1952 INVENTOR, By s. 0; ROBERTSON A1 1 s. mm;

ATTORNEY SPATIAL HARMONIC TRAVELING WAVE TUBE Sloan D. Robertson, FairHaven, N. J., assignor to Bell Telephone Laboratories, Incorporated, NewYork, N. Y., a corporation of New York Application December 30, 1952,Serial No. 328,580

4 Claims. (Cl. 315-35) This invention relates to microwave devices andmore particularly to such devices of the so-called traveling wave type.

The principal object of this invention is to provide a wave propagatingcircuit for traveling wave tubes operating at extremely shortwavelengths, which is relatively easy to manufacture and which isparticularly well adapted for use with circular electron beams.

Another object is to achieve broad band amplification in traveling wavetubes operating at super high frequencies without sacrificing powerdissipation capacity and simplicity of construction.

Helical traveling wave tubes, previous to this invention, havecustomarily amplified electromagnetic waves by surrounding an electronstream with a wire helix along which the waves propagate with an axialvelocity substantially the same as the velocity of the electron streamso that the wave extracts kinetic energy from the electrons. Such a tubeis admirably suited for operation at frequencies below, for instance,10,000 megacycles, since it combines a very large band width with goodgain while at the same time remains basically easy to manufacture. Asthe fre- States PatentD ice quency of operation is increased, however,radiation from A solution to many of the problems encountered at 0'these high frequencies is presented in an article A Spatial HarmonicTraveling Wave Amplifier for Six Millimeters Wavelength by S. Millman,appearing in the Proceedings of the Institute of Radio Engineers, volume39, page 1040, September 1951. tion of the spatial harmonic principle ofoperation than that which follows the reader is referred to thisarticle. Since, however, this principle is utilized in the presentinvention, a brief description of it will be given here.

For a more complete explana If an electron stream is alternatelyshielded from and exposed to a component of field intensity in the samedirection as that of a traveling electromagnetic wave, the wave canextract energy from the stream even though the wave travels at highervelocity, provided the alternate shielding occurs at the properintervals. This is accomplished by beaming the electrons in electricalproximity to regularly spaced wave propagating discontinuities, chosenso that there exists between them a component of electric field parallelto the direction of electron flow and so that no such component existsin the region over them. By adjusting the velocity of the electronstream, a given electron can be made to reach each interval betweendiscontinuities at a time when the electric field intensity'at thatpoint is the same as it was in the preceding interval when this electronarrived there. The electrons can thus be 2,820,170 Patented Jan. 14,1958 synchronized in phase with any wave which propagates along thesediscontinuities with a component of phase velocity parallel to thedirection of electron flow equal to the velocity of electrons, plus avelocity such that the electric field rotates any multiple of :360degrees, between successive intervals.

Tubes which have been built previous to now to incorporate the spatialharmonic principle represent a noticeable improvement over aconventional helical tube for millimeter wavelength since they are morerugged and otter better gain-band width product. None of them, however,is as easy to manufacture as might be desired and one purpose,therefore, of the present invention is to overcome this drawback.

In accordance with one aspect of this invention a wire helix, inconjunction with a conductively bounded wave guide, is adapted for useas a wave propagating circuit embodying the spatial harmonic principle.Such a structure incorporates many of the advantages of a conventionalhelical circuit and it offers additional advantages of its own. Aclearer understanding, however, of this and of the other specificembodiments shown herein, together with a better appreciation of thegeneral nature and objects of this invention, will best be gained from astudy of the accompanying drawings and the following detaileddescription thereof.

With reference to the drawings in general:

Fig. 1 is aperspective view of an embodimentof a spatial harmonic waveguiding circuit in which the spatial harmonic discontinuities areformed. by a plurality of transverse slot openings in a thin walled tubeaxially aligned with the direction of wave propagation-within arectangular wave guide;

Fig. 2 shows a cross section of the center portion of a secondembodiment of a wave guiding circuit in whicha rectangular wave guidesurrounds a wire helix axially aligned with the guide and separated fromone wall thereof by a sheet of dielectric material; and

Fig. 3 shows a side section of a backward wave oscillator in which thewave propagating circuit isa rectangular wave guide which includeswithin it a wire helix centered along the top wall of the guide.

Referring now more particularly to the drawings, Fig. .1 shows, by wayof example for purposes of illustration, a spatial harmonic wave guidingcircuit 10 which comprises a rectangular wave guide 11 within which ahollow cylindrical ridge, or tube, 12 is asymmetrically positioned. Cutthrough the wall of this ridge are a plurality of slot- "like openings13 which are regularly spaced in the direction of wave propagation andwhich, together with the metal between them, form a series ofslot-resonators. These openings serve to expose recurrently theelectrons, which may be beamed through the hollow center of tube 12, tothe electric field of an electromagnetic wave propagating throughcircuit 10 in order that amplification 'of the wave may take place, asexplained previously. They also serve to distort the electric fieldwithin the circuit so that a wave propagating in its fundamentaltransverse electric mode will have in their vicinity a componentoelectric field parallel to the electron flow.

The inside dimensions of guide 11 are preferably chosen so that atransverse electric wave may propagate'ther'ethrough in its fundamentalmode with the electric field perpendicular to the two wider walls of theguide. The straight center section of this guide surrounds ridge or tube12 which may be brazed along the center of the lower wider wall. Thewall thickness of this ridge is not critical but it should be many timesthe skin depth at the frequency of operation but still thin incomparison with the diameter of the ridge. The length of the slots cutthrough this wall should beroughly equalto. a, half-free spacewavelength at the upper cut-off frequency gof the circuit. Formechanical strength of the ridge, having openings as shown in "Fig. "1,the circumference of the ridge should be slightly greater than thislength. If desired, ridge .12 may be replaced by an equivalent wirehelix having appropriate pitch and diameter. At both ends of tube .12the guide is bent upward to provideimpedan ce matching between thecenter section of the circuit and the input and output connections whichmay, for example, be wave guides of the same cross section as guide '11connected directly to ends 14 and 15 of the circult. Openings inthecurved sections of the lower wall of guide 11 provide a free space forinserting tube 12 into the guide when the circuit is being assembled.and they permit electron stream 16 to be beamed through the hollowcenter of this tube when the .circuit is operating. Electron ,gun I7 andcollector electrode 18 are aligned with respect to circuit 10 so thatelectron stream 16 which flows between them passes axially through tube12. Identical envelopes 19 surround these electrodes and form, inConjunction with windows (not shown) in bothends of the guide and themetal walls thereof, an air-tight en- 'plosure surrounding the electronstream. A magnetic field, produced by means not shown but which may besimilar to magnets 50 and 51 shown in Fig. 3, is aligned with the axisof the electron stream for the purpose of confining the electrons to asmall region around the axis of the stream. The conducting elements ofcircuit 10 should be non-magnetic in order not to distort the magneticfield and they should preferably have the same coefiicient of expansionto minimize the etfects of heating.

Wave energy is preferably applied to circuit 10 by some appropriatemeans so that the electric field of the wave propagates through thecircuit perpendicular to the top wider wall of guide 11. As this wavepropagates from the input end (end 14) of the circuit to the output endit is amplified'by spatial harmonic interaction with the electron streamflowing through the center of tube 12. This spatial harmonic phenomenonhas been dealt with briefly in the foregoing, but a better understandingof it will be gained by consideration of the following shortmathematical analysis adapted specifically to the structure shown inFig. .1 but applicable to spatial harmonic action in general.

If 2. is the direction of wave velocity in the wave guide, then in thevicinity of recurrent discontinuities in the guide the 2 component of atraveling wave may be written where d is the distance between successivediscontinuities, which here are slots 13 in tube 12, n is an integer and9 is the phase delay in radians from one discontinuity to the next andis given by :where a is the guide wavelength of the fundamental wavecorresponding to 11:0 in Equation 2. Assuming the amplitude of E to beconstant at the edge of the discontinuities or slots, and denoting it byE A may be written tFg jpnflnew where w is the width of'a slot 13 intube 12 Substituting in Equation 1 From this last equation it can beseen that near the slot discontinuities in the wave guide there appearsto be an infinite number of spatial harmonic components of thefundamental wave, each traveling at a different phase velocity given bycod Err-n+0) in which n is an integer between and Setting 11:0 we seethat the fundamental wave travels in the positive 2. direction with aphase velocity of g 6 For n=1 a wave appears to travel in the positivez-direction with a velocity of and -lwhich is less "than the velocityfor the fundamental Wave. Similarly for other positive values of n. Forn=l there appears to be a wave traveling in the positive 2 directionwith a phase velocity cod -21r|9) which is negative since fundamentalphase displacement G'between successive slots is less than 2n. Thus foreach negative integer n there corresponds a wave having negativephase-velocity, or, in other words, a backward traveling Wave. The groupvelocity of all spatial harmonic Waves, it should be remembered, isalways in the direction of power propagation and is the same for all,including those which have negative phase velocity.

From an inspection of Fig. 1 it is apparent that somewhere between thecondition where the slot spacing d is zero, in which case there issubstantially no interaction between the electromagnetic wave and theelectron stream, and the condition where width w of slot opening iszero, in which case the interaction is likewise zero, there must be someratio of slot width to slot spacing which gives optimum interaction ifthere is to be any net gain. Now, it is easily shown that the electronvelocity V required for synchronization is given by and 21m+e) (6) wherew is the radian frequency, d center to center slot spacing, it aninteger and 0 the fundamental phase displacement between slots, usuallyIt can further be shown that the amplification of the electromagneticwave interacting with the electrons is proportional to tion with respectto w/d and setting the result equal to zero, the gain is seen to bemaximum when w 2.33 E 2m+e (8) As mentioned previously, practical valuesof 0 may be roughly between and so from Equations t6 and 8' w is easilydetermined for a given electron velocity V a given value of n and a.given frequency of operation.

The optimum slot-spacing and slot width of a structure designed for aparticular mode of spatial harmonic operation is determined fromEquations 6 and 8 but it should be understood that this same structuremay be used for operation in additional modes although with somewhatreduced efliciency. The number of slots used will depend upon the gaindesired but approximately 100 are ordinarily suificient. The followingdimensions will serve to indicate the size relationships of the variouselements of the structure shown in Fig. 1. Although these dimensionshave been found satisfactory in a circuit substantially the same as thatin Fig. 1 which has been built and tested, they are not given inlimitation but merely in illustration of possible values. Thesedimensions have been chosen for optimum interaction of the first spatialharmonic of a wave with an electron stream having a velocity roughlyequivalent to 1300 volts. The inside width and height of guide 11 are0.83M, and 0.41%, length of slot 13=0.46)\ width w=0.027 distanced=0.086 where t is the free space wavelength at the frequency ofoperation.

Fig. 2 shows a cross section of a center portion of a wave guidingcircuit 30 which is similar in operation to that shown in Fig. 1.Circuit 30 consists of a rectangular wave guide 31, which may be, but isnot necessarily, identical to guide 11 in Fig. 1, which surrounds wirehelix 32. This helix, which is separated from a wider wall of the guide31, corresponding to the lower wall of guide 11, by a sheet ofdielectric 33, may be thought of as equivalent to ridge 12 in Fig. 1.The pitch between turns of helix 32 corresponds to distance d and theopening between turns corresponds in width to width w of the openings inridge 12. The presence of dielectric material 33, which may for examplebe mica, permits the diameter of helix 32 to be approximately twice thediameter that ridge 12 may be made for a given frequency of operation.Thickness t of this dielectric, which is preferably uniform along thelength of the guide in order that helix 32 may be aligned parallel tothe axis thereof, may be chosen from a range having wide limits but avalue of roughly one-tenth the diameter of helix 32 'has been foundsatisfactory. The result of decreasing thickness t is -to lower thefrequency of operation for a given helix and wave guide. The turns ofwire forming helix 32, together with the spaces between them, form aseries of slot-resonators which are substantially the same as theresonators in Fig. 1. It is therefore apparent that helix 32 may bereplaced by a plurality of loops of wire which are transverse to thedirection of wave propagation and regularly spaced a distance d apart inthat direction.

In operation, an electron stream may be beamed through the center ofhelix 32 and a transverse electric wave may be applied to circuit 30 byan appropriate means, such as the curved end of guide 11 in Fig. 1. Waveenergy may then be extracted at the output end of the circuit by somesuitable means.

The wire helix shown in Fig. 2, as well as the parallel loop structure,is particularly adapted to backward spatial harmonic operation, sincethe ratio of space between the wire w to the wide pitch at can readilybe made to satisfy Equations 6 and 8 for negative integers. A ratio ofhas been found suitable in such a structure for synchronization of theelectron stream with the first backward wave. A smaller ratio in thevicinity of one-third should be used with the first forward wave.

It should be understood that none of the wave guiding circuits describedin the foregoing is limited to spatial harmonic wave amplification sinceany of these structures, if it has the required dimensions,'.may'be'ii'sed for the generation of wave energy either by conventional or bybackward wave operation. Conventional oscillations may be obtained inany amplifier simply by returning a suflicient portion of the outputenergy to the input of the amplifier and the operation of such anarrangement is so well known that more of a description here would besuperfluous. The generation of backward wave oscillations on the otherhand is a recent development in the art and in view of the importance ofthe present invention in this regard, a brief description of thebackward wave oscillator is appropriate.

-In Fig. 3 there is shown a side section of a backward wave oscillatorin which circuit 40 is the wave propagating element. This circuit isaligned with respect to electron gun 41 and collector cavity 42 so thatelectron stream 43 flows through the center ofhelix 44 which may bebrazed along the center of the top wider wall of rectangular guide 45.At the collector end of the circuit, lossy material 46 is positionedwithin guide 45 surrounding helix 44, in order to minimize reflection ofwave energy at this point. Any wave energy which may be returned fromthe output connection at the gun end of the circuit by impedancemismatches there is thus substantially reduced and its unwantedinterference with energy propagating in the opposite direction is mostlyeliminated. At the gun end of the circuit oscillating wave energy isextracted from the circuit by a continuation of guide 45 which is bentdownward for impedance matching as explained previously. An appropriateopening is provided in'the curved section of the top wall of this guidefor the passage of electron stream 43. Guide 45 is sealed throughenvelope 47 and this envelope, together with window 48 in the guide,envelope 49 and magnet poles 5's) and 51, form a gas-tight enclosuresurrounding the electron stream. Opening 42 in pole piece 51 is shapedapproximately as shown in order to reduce secondary emission from thismember which serves additionally as the collector electrode. All theelements in the region between pole pieces should be nonmagnetic so thatthe magnetic field may be made to focus the electron stream along anaxis with which the field is aligned.

When the current density of electron stream 43 in the arrangement shownin Fig. 3 exceeds a certain critical value, oscillations may suddenlybegin at a frequency which is determined by stream velocity. Wave energyoriginating at the collector end of circuit 40 flows toward the outputend thereof, where it is led ofi through window as to an appropriateoutput connection. As this energy passes along the helix within guide 45it is amplified by interaction between the backward traveling spatialharmonic of itself which is synchronized with the electron stream. Thisinteraction at the same time causes a bunching of the electron stream.This bunching in turn causes an increase in wave energy which in turncauses a bunching of the electron stream and so on. Thus the feedbackenergy necessary to sustain oscillations is automatically returned tothe circuit by the electron stream. Since the frequency of oscillationis determined principally by the electron stream velocity for a givenwave guiding structure and since this velocity is easily varied over awide range, the frequency may be modulated at a high rate and over avery broad band width.

The invention described herein is not limited solely to the embodimentsshown or described, since it may include wave guides of other thanrectangular cross section. Furthermore, the input and output connectionsdescribed above in connection with the drawings may be replaced byequivalent means without altering the nature of this invention. Lastly,it will be apparent to those skilled in the art that the dimensions ofthe wave guiding circuits shown in the accompanying drawings may beselected over a wide range without departing from the spirit or scope ofthe invention as set forth.

. What is claimed is:

1. lnanmicrowave device, means for beaming an elecrrenstream'along. apath, and wave guiding means adapted to propagate'therethrough in adirection parallel to said path anJeIectric wave for interaction withsaid electron stream, said waveguiding means including a wave guideasymmetrically surrounding a hollow cylindrical ridge having cut 'in itssurface a plurality of slot-resonators lyingttransverse to the directionof wave propagation and regularly spaced in that direction, the lateraldimensions of said ridge being less than the lateral dimensions of saidwave guide.

2. In a traveling. wave tube, means for forming and projecting anelectron stream, and conductively bounded wave guiding means including ahollow cylindrical tube connected along one wall within a rectangularwave guide and spaced from the remaining walls thereof and having inits'su'rface aplur'ality of slot-like openings transverse tothedirection of wave propagation and regularly spaced apart in thatdirection.

3. In a, traveling wave tube, means for forming and projecting anelectron stream, and conductively bounded wave guiding means including alength of rectangular waveguide whose ends are bent out of the line ofthe electron flow and whose center section surrounds a hollowcylindrical member lying along one wall and spaced from the remainingwalls thereof whose surface contains a "8 plurality ofslots formingslot-resonators lying substantially transverse to the direction of wavepropagation and which are regularly spaced in that direction.

4. In a microwave device,-means adapted to propagate therethrough anelectromagnetic wave at'a speed less than the speed of light, said meansincluding a raised cylindrical hollow ridge having cut in the surfacethereof a plurality of slot-like openings lying substantially transverseto the direction of wave propagation and spaced apart in that direction,and a rectangular wave guide asymmetrically surrounding said ridge, saidridge being spaced from at least three walls of said Wave guide.

References ited in the file of this patent UNITED STATES PATENTS2,395,560 Llewellyn Feb. 26, '1946 2,567,748 White Sept. 11, 19512,590,511 Craig et a1. Mar. 25, 1952 2,623,121 Loveridge Dec. 23, 19522,641,731 Lines June 9, 1953 2,647,175 Sheer July 28, 1953 2,708,236Pierce May 10, 1955 7 OTHER REFERENCES Article by I. R. Pierce, entitledMillimeter Waves," pp. 24-29 of Physics Today, for Nov. 1950.

